Problem: Simplify the following expression and state the condition under which the simplification is valid. $y = \dfrac{a^2 - 16}{a - 4}$
Solution: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = a$ $ b = \sqrt{16} = -4$ So we can rewrite the expression as: $y = \dfrac{({a} {-4})({a} + {4})} {a - 4} $ We can divide the numerator and denominator by $(a - 4)$ on condition that $a \neq 4$ Therefore $y = a + 4; a \neq 4$